Read the article in PDF (with tables): Risk Management Report on February Market Correction

February 6^{th}, 2018

**Findings**:

- 2 consecutive weekly losses greater than 3% is rare (1% of the time) and 3 consecutive losses is even more scarce (0.2% of the time)
- The 3 consecutive losses greater than 3% were always happening during recessionary period
- For 3 consecutive losses greater than 3%, even if investor exit the index position after the second week of loss, they would on average still save their investment by 6.11%. However, if investor is currently at the third week of consecutive losses, then perhaps it is too late to exit the market and actually is a good time to enter the market, as the market return in the next 4, 12, and 26 weeks are on average positive
- For 2 (but not 3) consecutive weekly losses greater than 3%, it is probably worth it to still be invested in the market and not rush exiting the market, especially when the market is at its 1-Year high level.
- When the market is at its all time high, it is more likely to have 2 consecutive weekly losses greater than 3% (4 events) rather than 3 consecutive losses (1 event)

**Conclusion:**

Current market correction could be a healthy correction instead of a sign for major recessionary period, based on the historical findings that it is unlikely for a recession to happen when the market is at its 1-Year high level. In a correction (2 consecutive weekly losses greater than 3%), it is also might not be worth the effort to do market timing and exit the market immediately, as the return following the exit at the second week is positive in the next 4, 12, and 26 weeks.

E-mail: kevin.yulianto@mail.mcgill.ca

**Historical Performance of S&P500 After Greater Than 3% Weekly Loss**

2017 was a very good year for the equity market around the globe and we began 2018 with a bullish outlook for the market, with the stock market reaching all time high. However, the recent -3.85% correction last week (Jan 29, 2018 to Feb 2, 2018) and Monday’s (Feb 5) drop of -4.1% in S&P500 index have intrigued investors whether another major correction is coming.

This short study aims to investigate the number of weekly loss greater than 2% and 3%, their average loss, and the performance afterwards for the S&P500 index in the period between February 1960 and February 2018. On the discussion below, it is also indicated whether such correction happens when the S&P500 is at its 1 year high, and the index performance afterwards if that is the case.

Using 3-month trailing standard deviation and under the assumption of normal distribution (not ideal, due to time constraint), we could calculate the rolling- 5% VaR for the portfolio and found that it was breached 190 times during the 3014 weeks period (6.3%). The occurrence rate of 6.3%, which is greater than our alpha of 5%, was mainly due to the normality assumption of the index return distribution. If the index weekly return is lower than the expected VaR on that particular week, the observation is recorded and later it was found that the average loss was -3.82% on a particular week, with the rolling – VaR ranging from 0.65% to 14.18%. The same calculation is applied using a cut-off value of -2% and -3%, the results are shown in Table 1.

As a forward-looking guidance, calculation on the index performance for 4, 12, and 26 weeks after a weekly loss greater than 3% was calculated. It was also found that 2 consecutive weekly losses greater than 3% is rare (1% of the time) and 3 consecutive losses is even more scarce (0.2% of the time).

Table 1. Summary of Loss

Table 2. Periods of 3 Consecutive Weekly Losses Greater than 3%

This study focuses on the events of 2 and 3 consecutive breach of the 3% loss limit and assess the performance of the index afterwards. Although it is premature to judge whether the market is going to close at a loss greater than 3% in the next 2 weeks (it closed with -3.85% loss last week), it is insightful to know what is expected to happen if it does. As you could see on Table 2, the 3 consecutive losses greater than 3% were always happening during recessionary period. Had investor been able to exit the market after the initial weekly loss, they would save 15.41% on average in the next 4 weeks after, 11.57% in the next 12 weeks after, and 6.22% in the 26 weeks after. However, this number is skewed by the return during 2009 period where the 3 consecutive losses were followed by strong rebound by the market.

The most relevant observation is perhaps related to the 1987 period, when the S&P500 index is at its 1-year high level (as it does now) and the correction proves to be a major one. The conclusion from this graph is that even if investor exit the index position after the second week of losses greater than 3%, they would on average still save their investment by 6.11% (13.11%, 11.87%, -0.74%, 0.2%). However, if it was already in the third week of consecutive losses, then perhaps it is too late to exit the market and actually is a good time to enter the market, as the market return in the next 4, 12, and 26 weeks are on average positive.

Now let’s take a look at what happened if there is 2 consecutive loss greater than 3% in the market, which is more relevant to current situation where the market could potentially do this week.

When the market had 2 consecutive weekly losses greater than 3%, then on average investors could save 1.76% in the next 4 weeks by exiting their position in the index after the initial loss. However, on a longer time period, the 12 weeks and 26 weeks return after the initial weekly loss is actually positive at 3.31% and 8.44% respectively. This means that for 2 (but not 3) consecutive weekly losses greater than 3%, it is probably worth it to still be invested in the market and not rush exiting the market, especially when the market is at its 1-Year high level.

Recapitulating from the frequency of 2 and 3 consecutive losses, when the market is at its all time high, it is more likely to have 2 consecutive weekly losses greater than 3% (4 events) rather than 3 consecutive losses (1 event). Hence, without deeper fundamental economic research, I would conclude that the odd is in our favor.

My conclusion from this short study is that the current market correction could potentially be a healthy correction and does not necessarily means a recession is coming.

Table 3. Periods of 2 Consecutive Weekly Losses Greater than 3%